### Tamilnadu Board Business Maths Question papers for 12th Standard (English Medium) Question paper & Study Materials

#### 12th Standard Business Maths - Random Variable and Mathematical Expectation Model Question Paper - by Ranganathan - Arakkonam - Oct 09, 2019 - View & Read

• 1)

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called

• 2)

Probability which explains x is equal to or less than particular value is classified as

• 3)

A variable that can assume any possible value between two points is called

• 4)

If c is a constant, then E(c) is

• 5)

E[X-E(X)] is equal to

#### 12th Standard Business Maths - Numerical Methods Model Question Paper - by Ranganathan - Arakkonam - Oct 09, 2019 - View & Read

• 1)

Δ2y0 =

• 2)

Δf(x) =

• 3)

If m and n are positive integers then ΔmΔnf(x) =

• 4)

E f (x)=

• 5)

∇ f(a) =

#### 12th Standard Business Maths - Differential Equations Model Question Paper - by Ranganathan - Arakkonam - Oct 01, 2019 - View & Read

• 1)

The degree of the differential equation $\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3$

• 2)

The complementary function of (D2+ 4)y = e2x is

• 3)

If sec2 x is an integrating factor of the differential equation $\frac { dy }{ dx }$ + Py Q then P =

• 4)

The differential equation of x+ y= a2

• 5)

A homogeneous differential equation of the form  $\frac { dy }{ dx }$ = f$\left( \frac { y }{ x } \right)$ can be solved by making substitution,

#### 12th Standard - Business Maths Integral Calculus – II Model Question Paper - by Ranganathan - Arakkonam - Oct 01, 2019 - View & Read

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

The demand and supply functions are given by D(x)= 16 − x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is

• 3)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 4)

The demand function for the marginal function MR = 100 − 9x2 is

• 5)

The producer’s surplus when the supply function for a commodity is P = 3 + x and x0 = 3 is

#### 12th Business Maths - Operations Research Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Obtain the initial solution for the following problem

• 2)

Determine an initial basic feasible solution to the following transportation problem using North West corner rule.

Here Oi and Dj represent ith origin and jth destination.

• 3)

Obtain an initial basic feasible solution to the following transportation problem using least cost method.

Here Oi and Dj denote ith origin and jth destination respectively.

• 4)

Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method

Cost are expressed in terms of rupees per unit shipped.

• 5)

Find the initial basic feasible solution for the following transportation problem by VAM

#### 12th Business Maths - Applied Statistics Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Fit a trend line by the method of freehand method for the given data

 Year 2000 2001 2002 2003 2004 2005 2006 2007 Sales 30 46 25 59 40 60 38 65
• 2)

Fit a trend line by the method of semi-averages for the given data.

 Year 2000 2001 2002 2003 2004 2005 2006 Production 105 115 120 100 110 125 135
• 3)

Fit a trend line by the method of semi-averages for the given data.

 Year 1990 1991 1992 1993 1994 1995 1996 1997 Sales 15 11 20 10 15 25 35 30
• 4)

Given below are the data relating to the production of sugarcane in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.

 Year 2000 2001 2002 2003 2004 2005 2006 Prod. of Sugarcane 40 45 46 42 47 50 46
• 5)

Given below are the data relating to the sales of a product in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.

 Year 1995 1996 1997 1998 1999 2000 2001 2002 Sales 6.7 5.3 4.3 6.1 5.6 7.9 5.8 6.1

#### 12th Business Maths - Sampling Techniques and Statistical Inference Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Using the Kendall-Babington Smith - Random number table,Draw5 random samples.

 23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44 05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43 14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34 38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95 97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13
• 2)

Using the following Tippett’s random number table,

 2952 6641 3992 9792 7969 5911 3170 5624 4167 9524 1545 1396 7203 5356 1300 2693 2670 7483 3408 2762 3563 1089 6913 7991 0560 5246 1112 6107 6008 8125 4233 8776 2754 9143 1405 9025 7002 6111 8816 6446

Draw a sample of 15 houses from Cauvery Street which has 83 houses in total.

• 3)

Using the following random number table,

 Tippet’s random number table 2952 6641 3992 9792 7969 5911 3170 5624 4167 9524 1545 1396 7203 5356 1300 2693 2670 7483 3408 2762 3563 1089 6913 7991 0560 5246 1112 6107 6008 8125 4233 8776 2754 9143 1405 9025 7002 6111 8816 6446

Draw a sample of 10 children with theirheight from the population of 8,585 children as classified hereunder.

 Height (cm) 105 107 109 111 113 115 117 119 121 123 125 Number of children 2 4 14 41 83 169 394 669 990 1223 1329 Height(cm) 127 129 131 133 135 137 139 141 143 145 No. of children 1230 1063 646 392 202 79 32 16 5 2
• 4)

Using the following random number table (Kendall-Babington Smith)

 23 15 75 48 59 01 83 72 59 93 76 24 97 08 86 95 23 03 67 44 05 54 55 50 43 10 53 74 35 08 90 61 18 37 44 10 96 22 13 43 14 87 16 03 50 32 40 43 62 23 50 05 10 03 22 11 54 36 08 34 38 97 67 49 51 94 05 17 58 53 78 80 59 01 94 32 42 87 16 95 97 31 26 17 18 99 75 53 08 70 94 25 12 58 41 54 88 21 05 13

Draw a random sample of 10 four- figure numbers startingfrom 1550 to 8000.

• 5)

From the following data, select 68 random samples from the populationof heterogeneous group with size of 500 through stratified random sampling, considering the following categories as strata.
Category1: Lower income class -39%
Category2: Middle income class - 38%
Category3: Upper income class- 23%

#### 12th Business Maths - Probability Distributions Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

In tossing of a five fair coin, find the chance of getting exactly 3 heads.

• 2)

The mean of Binomials distribution is 20 and standard deviation is 4. Find the parameters of the distribution.

• 3)

If x is a binomially distributed random variable with E(x) =2 and van (x)=4/3 Find P(x=5)

• 4)

The sum and product of the mean and variance of a binomial distribution are 24 and 128. Find the distribution.

• 5)

Suppose A and B are two equally strong table tennis players. Which of the following two events is more probable:
(a) A beats B exactly in 3 games out of 4 or
(b) A beats B exactly in 5 games out of 8 ?

#### 12th Business Maths - Random Variable and Mathematical Expectation Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

The number of cars in a household is given below.

 No. of cars 0 1 2 3 4 No. of Household 30 120 380 190 80
• 2)

A random variable X has the following probability function

 Values of X 0 1 2 3 4 5 6 7 p(x) 0 a 2a 2a 3a a2 2a2 7a2+a
• 3)

If $p(x)\begin{cases} \underline { x } , \\ 20 \\ 0, \end{cases}x=$0,1,2,3,4,5
Find (i) P(X<3) and (ii) P(2$\le$4)

• 4)

Two unbiased dice are thrown simultaneously and sum of the upturned faces considered as random variable. Construct a probability mass function.

• 5)

A coin is tossed thrice. Let Xbe the number of observed heads. Find the cumulative distribution function of X.

#### 12th Business Maths - Numerical Methods Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Construct a forward difference table for the following data

 x 0 10 20 30 y 0 0.174 0.347 0.518
• 2)

Construct a forward difference table for y = f(x) = x3+2x+1 for x = 1,2,3,4,5

• 3)

By constructing a difference table and using the second order differences as constant, find the sixth term of the series 8,12,19,29,42…

• 4)

Find (i) Δeax
(ii) Δ2ex
(iii) Δ log x

• 5)

Evaluate $\Delta$$\left[ \frac { 5x+12 }{ { x }^{ 2 }+5x+6 } \right]$ by taking ‘1’ as the interval of differencing.

#### 12th Business Maths - Differential Equations Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Find the differential equation of all circles x2 +y2 + 2gx = 0 which pass through the origin and whose centres are on the X-axis.

• 2)

Form the differential equation for $\frac { { x }^{ 2 } }{ { a }^{ 2 } } +\frac { { y }^{ 2 } }{ { b }^{ 2 } }$=1 where a & b are arbitrary constants.

• 3)

Form the differential equation for y=(A+Bx)e3x where A and B are constants.

• 4)

Solve: sec 2x dy - sin 5x sec2 y dx = 0

• 5)

Solve: cos2x dy + y.etanx dx=0

#### 12th Business Maths - Integral Calculus – II Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Find the area bounded by y = 4x + 3 with x- axis between the lines x = 1 and x = 4

• 2)

Find the area of the region bounded by the line x − 2y − 12 = 0 , the y-axis and the lines y = 2, y = 5.

• 3)

Find the area of the region bounded by the parabola $y=4{ - }x^{ 2 }$ , x −axis and the lines x = 0, x = 2

• 4)

Find the area bounded by y = x between the lines x = −1 and x = 2 with x -axis.

• 5)

Sketch the graph $y=\left| x+3 \right|$ and evaluate $\int _{ -6 }^{ 0 }{ \left| x+3 \right| }$ dx.

#### 12th Business Maths - Integral Calculus – I Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Evaluate  $\int { \frac { { { x }^{ 4 }+{ x }^{ 4 }+1 } }{ { x }^{ 2 }-x+1 } }$

• 2)

Evaluate $\int { \frac { cos2x-cos2\alpha }{ cosx-cos\alpha } } dx$

• 3)

Evaluate $\int { \frac { { ({ a }^{ x }{ +b }^{ x }) }^{ 2 } }{ { a }^{ x }b^{ x } } dx }$

• 4)

If f' (x) = 3x2 - $\frac { 2 }{ { x }^{ 3 } }$ and f(1) = 0, find f(x)

• 5)

Evaluate $\int { \frac { { 8 }^{ 1+x }+{ 4 }^{ 1-x } }{ { 2 }^{ x } } } dx$

#### 12th Business Maths - Applications of Matrices and Determinants Three Marks Questions - by Sridevi - Sankarankoil - Oct 01, 2019 - View & Read

• 1)

Find the rank of the matrix
$A=\left( \begin{matrix} 2 & 4 & 5 \\ 4 & 8 & 10 \\ -6 & -12 & -15 \end{matrix} \right)$

• 2)

Findtherankofthematrix $A=\left( \begin{matrix} 1 & 2 & -4 \\ 2 & -1 & 3 \\ 8 & 1 & 9 \end{matrix}\begin{matrix} 5 \\ 6 \\ 7 \end{matrix} \right)$

• 3)

Show that the equations 2x - Y + z = 7, 3x +y- 5z = 13, x +y + z = 5 are consistent and have a unique solution.

• 4)

Show that the equations x + 2y = 3, Y - z = 2, x +y + z = 1 are consistent and have infinite sets of solution.

• 5)

Show that the equations x- 3y + 4z = 3, 2x - 5y + 7z = 6, 3x - 8y + 11z = 1 are inconsistent

#### 12th Standard Business Maths - Integral Calculus – I Model Question Paper - by Ranganathan - Arakkonam - Sep 27, 2019 - View & Read

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

$\frac { sin5x-sinx }{ cos3x }$dx

• 3)

$\sqrt { { e }^{ x } }$ dx is

• 4)

$\Gamma (n)$ is

• 5)

$\int { \left( x-1 \right) } { e }^{ -x }$ dx = __________ +c

#### 12th Business Maths - Applications of Matrices and Determinants Model Question Paper - by Ranganathan - Arakkonam - Sep 27, 2019 - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of the unit matrix of order n is

• 3)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 4)

Which of the following is not an elementary transformation?

• 5)

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

#### 12th Standard Business Maths - Operations Research Two Marks Questions - by Sridevi - Sankarankoil - Sep 21, 2019 - View & Read

• 1)

Determine an initial basic feasible solution of the following transportation problem by north west corner method

• 2)

Obtain an initial basic feasible solution to the following transportation problem by using least- cost method.

• 3)

Consider the following transportation problem

Determine initial basic feasible solution by VAM

• 4)

Obtain an initial basic feasible solution to the following transportation problem by north west corner method.

• 5)

Give mathematical form of assignment problem.

#### 12th Business Maths - Applied Statistics Two Marks Quesions - by Sridevi - Sankarankoil - Sep 21, 2019 - View & Read

• 1)

Explain cyclic variations.

• 2)

• 3)

Define seasonal index.

• 4)

State the two normal equations used in fitting a straight line.

• 5)

State the different methods of measuring trend.

#### 12th Business Maths - Sampling Techniques and Statistical Inference Two Marks Questions - by Sridevi - Sankarankoil - Sep 21, 2019 - View & Read

• 1)

Explain in detail about simple random sampling with a suitable example.

• 2)

Explain the stratified random sampling with a suitable example.

• 3)

Explain in detail about systematic random sampling with example.

• 4)

State any three merits of stratified random sampling.

• 5)

State any two demerits of systematic random sampling.

#### 12th Business Maths - Term 1 Model Question Paper - by Ranganathan - Arakkonam - Sep 21, 2019 - View & Read

• 1)

The rank of m×n matrix whose elements are unity is

• 2)

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

• 3)

$\frac { { 2x }^{ 3 } }{ 4+{ x }^{ 4 } }$dx is

• 4)

$\int _{ 0 }^{ \frac { \pi }{ 3 } }{ tanx } dx$ is

• 5)

If the marginal revenue MR = 35 + 7x − 3x2, then the average revenue AR is

#### 12th Business Maths - Probability Distributions Two Marks Question - by Sridevi - Sankarankoil - Sep 19, 2019 - View & Read

• 1)

In a family of 3 children, what is the probability that there will be exactly 2 girls?

• 2)

Defects in yarn manufactured by a local mill can be approximated by a distribution with a mean of 1.2 defects for every 6 metres of length. If lengths of 6 metres are to be inspected, find the probability of less than 2 defects.

• 3)

A pair of dice is thrown 4 times. If getting a doublet is considered a success, find the probability of 2 successes.

• 4)

The mean of a binomial distribution is 5 and standard deviation is 2. Determine the distribution.

• 5)

Write any 2 examples for Poisson distribution.

#### 12th Business Maths - Random Variable and Mathematical Expectation Two Marks Question - by Sridevi - Sankarankoil - Sep 19, 2019 - View & Read

• 1)

The discrete random variable X has the following probability function
P(X=x)={$\\ \\ kx\quad \quad \quad \quad x=2,4,6\\ k(x-2)\quad x=8\\ 0\quad \quad\quad \quad otherwisde$
where k is a constant. Show that k=$\frac{1}{18}$

• 2)

The discrete random variable X has the probability function

 X 1 2 3 4 P(X=x) k 2k 3k 4k

Show that k =0.1.

• 3)

A continuous random variable X has the following distribution function:
F(x)={$0\quad \quad \quad \quad ,if\quad x\le 1\\ k(x-1{ ) }^{ 4 },if13$
Find (i) k and (ii) the probability density function.

• 4)

What do you understand by continuous random variable?

• 5)

Describe what is meant by a random variable.

#### 12th Business Maths Chapter 5 Numerical Methods Two Marks Question - by Sridevi - Sankarankoil - Sep 19, 2019 - View & Read

• 1)

Evaluate ∆(log ax).

• 2)

If y = x− x+ x − 1 calculate the values of y for x = 0,1,2,3,4,5 and form the forward differences table.

• 3)

Evaluate Δ$\left[ \frac { 1 }{ (x+1)(x+2) } \right]$ by taking ‘1’ as the interval of differencing

• 4)

Using graphic method, find the value of y when x = 48 from the following data:

 x 40 50 60 70 y 6.2 7.2 9.1 12
• 5)

Using Newton’s forward interpolation formula find the cubic polynomial.

 x 0 1 2 3 f(x) 1 2 1 10

#### 12th Business Maths Chapter 4 Differential Equations Two Marks Question - by Sridevi - Sankarankoil - Sep 19, 2019 - View & Read

• 1)

Form the differential equation by eliminating α and β from (x − α)2 + (y − β)2 = r2

• 2)

Find the differential equation of the family of all straight lines passing through the origin.

• 3)

Solve the following differential equations (D2+D−6)y=e3x + e−3x

• 4)

Solve the following differential equations (D2−10D+25)y=4e5x + 5

• 5)

Solve (D2-3D+2)y =e4x given y=0 when x=0 and x=1.

#### 12th Standard Business Maths Chapter 3 Integral Calculus – II Two Marks Questions - by Sridevi - Sankarankoil - Sep 16, 2019 - View & Read

• 1)

The marginal cost function is MC = 300 ${ x }^{ \frac { 2 }{ 5 } }$ and fixed cost is zero. Find out the total cost and average cost functions.

• 2)

If the marginal cost function of x units of output is $\frac { a }{ \sqrt { ax+b } }$ and if the cost of output is zero. Find the total cost as a function of x.

• 3)

If the marginal cost (MC) of a production of the company is directly proportional to the number of units (x) produced, then find the total cost function, when the fixed cost is Rs. 5,000 and the cost of producing 50 units is Rs. 5,625.

• 4)

The demand function p = 85 − 5x and supply function p = 3x − 35. Calculate the equilibrium price and quantity demanded .Also calculate consumer’s surplus.

• 5)

The demand and supply functions under perfect competition are p= 1600 − x2 and ps = 2x2 + 400 respectively. Find the producer’s surplus.

#### 12th Business Maths Unit 2 Integral Calculus – I Two Marks Questions - by Sridevi - Sankarankoil - Sep 16, 2019 - View & Read

• 1)

Integrate the following with respect to x.

$\frac { 8x+13 }{ \sqrt { 4x+7 } }$

• 2)

Integrate the following with respect to x.

$\frac { 1 }{ \sqrt { x+1 } +\sqrt { x-1 } }$

• 3)

Integrate the following with respect to x.
$\frac { { x }^{ 3 } }{ x+2 }$

• 4)

$If\quad f' \prime x=\frac { 1 }{ x } andf(1)=\frac { \pi }{ 4 } ,\quad then\quad findf(x)$

• 5)

Integrate the following with respect to x.
$\frac { { e }^{ 3x }+{ e }^{ 5x } }{ { e }^{ x }+{ e }^{ -x } }$

#### 12th Business Maths - Applications of Matrices and Determinants Two Marks Questions - by Sridevi - Sankarankoil - Sep 16, 2019 - View & Read

• 1)

Solve the following system of equations by rank method
x+y+z=9,2x+5y+7z=52,2x−y−z =0

• 2)

For what values of the parameterl , will the following equations fail to have unique
solution: 3x−y+lz=1,2x+y+z=2,x+2y−lz = −1 by rank method.

• 3)

An amount of 5,000/- is to be deposited in three different bonds bearing 6%, 7%
and 8% per year respectively. Total annual income is 358/-. If the income from
first two investments is `70/- more than the income from the third, then find the
amount of investment in each bond by rank method.

• 4)

Two types of soaps A and B are in the market. Their present market shares are 15% for A and 85% for B. Of those who bought A the previous year, 65% continue to buy it again while 35% switch over to B. Of those who bought B the previous year, 55% buy it again and 45% switch over to A. Find their market shares after one year and when is the equilibrium reached?

• 5)

Find k if the equations 2x+3y−z=5,3x−y+4z=2,x+7y−6z=k are consistent.

#### 12th Business Maths - Term 1 Five Mark Model Question Paper - by Sridevi - Sankarankoil - Sep 16, 2019 - View & Read

• 1)

Solve the equations 2x + 3y = 7, 3x + 5y = 9 by Cramer’s rule.

• 2)

The price of 3 Business Mathematics books, 2 Accountancy books and one
Commerce book is Rs840. The price of 2 Business Mathematics books, one Accountancy
book and one Commerce book is Rs 570. The price of one Business Mathematics book, one
Accountancy book and 2 Commerce books is Rs 630. Find the cost of each book by using
Cramer’s rule.

• 3)

Evaluate $\int { \frac { 7x-1 }{ { x }^{ 2 }-5x+6 } dx }$

• 4)

A company produces 50,000 units per week with 200 workers. The rate of change of productions with respect to the change in the number of additional labour x is represented as 300 - 5x1/2 If 64 additional labours are employed, find out the additional number of units, the company can produce.

• 5)

Solve 3extan ydx +(1 + ex)sec2ydy = 0 given y(0) = $\frac { \pi }{ 4 }$

#### 12th Business Maths Quarterly Model Question Paper - by Sridevi - Sankarankoil - Sep 13, 2019 - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is

• 3)

For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

• 4)

If A, B are two n x n non-singular matrices, then

• 5)

$\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$ dx is

#### 12th Business Maths Unit 10 Operations Research Book Back Questions - by Sridevi - Sankarankoil - Sep 05, 2019 - View & Read

• 1)

The transportation problem is said to be unbalanced if _________

• 2)

Solution for transportation problem using __________method is nearer to an optimal solution.

• 3)

In an assignment problem the value of decision variable xij is _________

• 4)

If number of sources is not equal to number of destinations, the assignment problem is called____________

• 5)

The solution for an assignment problem is optimal if

#### 12th Business Maths Chapter 9 Applied Statistics Book Back Questions - by Sridevi - Sankarankoil - Sep 05, 2019 - View & Read

• 1)

A time series is a set of data recorded

• 2)

The value of ‘b’ in the trend line y=a+bx is

• 3)

The component of a time series attached to long term variation is trended as

• 4)

Laspeyre’s index = 110, Paasche’s index = 108, then Fisher’s Ideal index is equal to:

• 5)

Which of the following Index number satisfy the time reversal test?

#### 12th Business Maths - Sampling Techniques and Statistical Inference Book Back Questions - by Sridevi - Sankarankoil - Sep 05, 2019 - View & Read

• 1)

A …………. may be finite or infinite according as the number of observations or items in it is finite or infinite.

• 2)

A finite subset of statistical individuals in a population is called __________

• 3)

Any statistical measure computed from sample data is known as ____________

• 4)

In simple random sampling from a population of units, the probability of drawing any unit at the first draw is

• 5)

In ___________ the heterogeneous groups are divided into homogeneous groups.

#### 12th Standard Business Maths Unit 7 Probability Distributions Book Back Questions - by Sridevi - Sankarankoil - Sep 04, 2019 - View & Read

• 1)

Normal distribution was invented by

• 2)

If Z is a standard normal variate, the proportion of items lying between Z = –0.5 and Z = –3.0 is

• 3)

An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be at least four successes is

• 4)

If for a binomial distribution b(n,p) mean = 4 and variance = 4/3, the probability, P(X ≥ 5) is equal to :

• 5)

The average percentage of failure in a certain examination is 40. The probability that out of a group of 6 candidates atleast 4 passed in the examination are:

#### 12th Standard Business Maths - Random Variable and Mathematical Expectation Book Back Questions - by Sridevi - Sankarankoil - Sep 04, 2019 - View & Read

• 1)

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called

• 2)

Probability which explains x is equal to or less than particular value is classified as

• 3)

If X is a discrete random variable and p x ( ) is the probability of X , then the expected value of this random variable is equal to

• 4)

Which of the following is not possible in probability distribution?

• 5)

A discrete probability distribution may be represented by

#### 12th Standard Business Maths Differential Equations Book Back Questions - by Sridevi - Sankarankoil - Sep 03, 2019 - View & Read

• 1)

The degree of the differential equation $\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3$

• 2)

The differential equation formed by eliminating a and b from y=ae+ be−x is

• 3)

The differential equation of y = mx + c is (m and c are arbitrary constants)

• 4)

The integrating factor of x $\frac { dy }{ dx }$ - y = x2 is

• 5)

The differential equation of x+ y= a2

#### 12th Standard Business Maths Unit 5 Numerical Methods Book Back Questions - by Sridevi - Sankarankoil - Sep 03, 2019 - View & Read

• 1)

Δ2y0 =

• 2)

If ‘n’ is a positive integer Δn[ Δ-n​ ​​​​​​f(x)]

• 3)

∇ f(a) =

• 4)

Lagrange’s interpolation formula can be used for

• 5)

If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x)

#### 12th Standard Business Maths Unit 3 Integral Calculus – II Book Back Questions - by Sridevi - Sankarankoil - Sep 03, 2019 - View & Read

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

• 3)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 4)

The profit of a function p(x) is maximum when

• 5)

When x0 = 5 and p0 = 3 the consumer’s surplus for the demand function pd = 28 − x2 is

#### 12th Standard Business Maths Unit 1 Integral Calculus – I Book Back Questions - by Sridevi - Sankarankoil - Aug 31, 2019 - View & Read

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

$\frac{logx}{x}$dx , x > 0 is

• 3)

$\left[ \frac { 9 }{ x-3 } -\frac { 1 }{ x+1 } \right]$dx is

• 4)

$\int _{ 0 }^{ 1 }{ (2x+1) } dx$ is

• 5)

$\int _{ -1 }^{ 1 }{ { x }^{ 3 }{ e }^{ { x }^{ 4 } } }$ dx is

#### 12th Standard Business Maths Unit 1 Applications of Matrices and Determinants Book Back Questions - by Sridevi - Sankarankoil - Aug 30, 2019 - View & Read

• 1)

The system of linear equations x+y+z=2,2x+y−z=3,3x+2y+k =4 has unique solution, if k is not equal to

• 2)

Cramer’s rule is applicable only to get an unique solution when

• 3)

if $\frac { { a }_{ 1 } }{ x } +\frac { { b }_{ 1 } }{ y } ={ c }_{ 1 },\frac { { a }_{ 2 } }{ x } +\frac { { b }_{ 2 } }{ y } ={ c }_{ 2 },{ \triangle }_{ 1= }\begin{vmatrix} { a }_{ 1 } & { b }_{ 1 } \\ { a }_{ 2 } & { b }_{ 2 } \end{vmatrix};\quad { \triangle }_{ 2 }=\begin{vmatrix} { b }_{ 1 } & { c }_{ 1 } \\ { b }_{ 2 } & { c }_{ 2 } \end{vmatrix}{ \triangle }_{ 3 }=\begin{vmatrix} { c }_{ 1 } & { a }_{ 1 } \\ { c }_{ 2 } & a_{ 2 } \end{vmatrix}$ then (x,y) is

• 4)

$\left| { A }_{ n\times n } \right|$=3 $\left| adjA \right|$ =243 then the value n is

• 5)

Rank of a null matrix is

#### 12th Standard Business Maths Unit 8 Applied Statistics One Mark Question with Answer Key - by Sridevi - Sankarankoil - Aug 29, 2019 - View & Read

• 1)

A time series is a set of data recorded

• 2)

A time series consists of

• 3)

The components of a time series which is attached to short term fluctuation is

• 4)

Factors responsible for seasonal variations are

• 5)

The additive model of the time series with the components T, S, C and I is

#### 12th Standard Business Maths - Sampling Techniques and Statistical Inference One Mark Question and Answer - by Sridevi - Sankarankoil - Aug 29, 2019 - View & Read

• 1)

A …………. may be finite or infinite according as the number of observations or items in it is finite or infinite.

• 2)

A __________ of statistical individuals in a population is called a sample.

• 3)

A finite subset of statistical individuals in a population is called __________

• 4)

Any statistical measure computed from sample data is known as ____________

• 5)

A_________is one where each item in the universe has an equal chance of known opportunity of being selected.

#### 12th Standard Business Maths - Probability Distributions One Mark Question and Answer - by Sridevi - Sankarankoil - Aug 28, 2019 - View & Read

• 1)

Normal distribution was invented by

• 2)

If X ~N(9,81) the standard normal variate Z will be

• 3)

In turning out certain toys in a manufacturing company, the average number of defectives is 1%. The probability that the sample of 100 toys there will be 3 defectives is

• 4)

The parameters of the normal distribution $f(x)=\left( \frac { 1 }{ \sqrt { 72\pi } } \right) \frac { { e }^{ -(x-10)^{ 2 } } }{ 72 } -\infty <X<\infty$

• 5)

A manufacturer produces switches and experiences that 2 per cent switches are defective. The probability that in a box of 50 switches, there are atmost two defective is :

#### 12th Business Maths Unit 6 Random Variable and Mathematical Expectation One Mark Question and Answer - by Sridevi - Sankarankoil - Aug 27, 2019 - View & Read

• 1)

Value which is obtained by multiplying possible values of random variable with probability of occurrence and is equal to weighted average is called

• 2)

Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0⋅ 29, 0⋅ 40, 0⋅ 35. Pofit per unit is 0⋅ 50 paisa then expected profits for three days are

• 3)

Probability which explains x is equal to or less than particular value is classified as

• 4)

Given E(X) = 5 and E(Y) = -2, then E(X – Y) is

• 5)

A variable that can assume any possible value between two points is called

#### 12th Business Maths Chapter 5 Numerical Methods One Mark Question and Answer - by Sridevi - Sankarankoil - Aug 27, 2019 - View & Read

• 1)

Δ2y0 =

• 2)

Δf(x) =

• 3)

∇ ≡

• 4)

∇ f(a) =

• 5)

For the given points (x0, y0) and (x1,y1) the Lagrange’s formula is

#### 12th Business Maths Unit 4 Differential Equations One Mark Question and Answer - by Sridevi - Sankarankoil - Aug 27, 2019 - View & Read

• 1)

The degree of the differential equation $\frac { { d }^{ 4 }y }{ { dx }^{ 4 } } { -\left( \frac { { d }^{ 2 }y }{ { dx }^{ 2 } } \right) }^{ 4 }+\frac { dy }{ dx } =3$

• 2)

The differential equation formed by eliminating a and b from y=ae+ be−x is

• 3)

The complementary function of (D2+ 4)y = e2x is

• 4)

The differential equation of y = mx + c is (m and c are arbitrary constants)

• 5)

The differential equation satisfied by all the straight lines in xy plane is

#### 12th Business Maths Unit 3 Integral Calculus – II One Mark Question Paper with Answer Key - by Sridevi - Sankarankoil - Aug 26, 2019 - View & Read

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

Area bounded by the curve y = e−2x between the limits 0 ≤ x ≤ ∞ is

• 3)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 4)

If the marginal revenue MR = 35 + 7x − 3x2, then the average revenue AR is

• 5)

The profit of a function p(x) is maximum when

#### 12th Standard Business Maths Unit 2 Integral Calculus – I One Mark Question Paper - by Sridevi - Sankarankoil - Aug 24, 2019 - View & Read

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

$\frac { { e }^{ x } }{ \sqrt { { 1+e }^{ x } } }$dx is

• 3)

$\frac { { e }^{ x } }{ { e }^{ x }+1 }$ dx

• 4)

$\int _{ 2 }^{ 4 }{ \frac { dx }{ x } }$ is

• 5)

The value of $\int _{ \frac { \pi }{ 2 } }^{ \frac { \pi }{ 2 } }{ cosx }$ dx is

#### 12th Business Maths Chapter 1 Applications of Matrices and Determinants One Mark Question Paper - by Sridevi - Sankarankoil - Aug 23, 2019 - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of the unit matrix of order n is

• 3)

Which of the following is not an elementary transformation?

• 4)

The system of equations 4x+6y=5, 6x+9y=7 has

• 5)

if $\left| A \right| \neq 0,$ then A is

#### 12th Business Maths Chpater 6 Random Variable and Mathematical Expectation Model Question Paper - by Sridevi - Sankarankoil - Aug 20, 2019 - View & Read

• 1)

A variable that can assume any possible value between two points is called

• 2)

A discrete probability distribution may be represented by

• 3)

If we have f(x)=2x, 0$\le$x$\le$1, then f (x) is a

• 4)

A set of numerical values assigned to a sample space is called

• 5)

The distribution function F(x) is equal to

#### 12th Standard Business Maths Chapter 5 Numerical Methods Model Question Paper - by Sridevi - Sankarankoil - Aug 05, 2019 - View & Read

• 1)

Δf(x) =

• 2)

If m and n are positive integers then ΔmΔnf(x) =

• 3)

∇ f(a) =

• 4)

Lagrange’s interpolation formula can be used for

• 5)

If f (x)=x+ 2x + 2 and the interval of differencing is unity then Δf (x)

#### 12th Standard Business Maths First Mid Term Model Question Paper - by Sridevi - Sankarankoil - Aug 01, 2019 - View & Read

• 1)

The rank of m×n matrix whose elements are unity is

• 2)

If the number of variables in a non- homogeneous system AX = B is n, then the system possesses a unique solution only when

• 3)

$\sqrt { { e }^{ x } }$ dx is

• 4)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 5)

If MR = 15 - 8x, then the revenue function is

#### 12th Standard Business Maths Differential Equations Important Question Paper - by Sridevi - Sankarankoil - Jul 30, 2019 - View & Read

• 1)

The differential equation ${ \left( \frac { dx }{ dy } \right) }^{ 3 }+2{ y }^{ \frac { 1 }{ 2 } }$ = x is

• 2)

The integrating factor of the differential equation $\frac{dx}{dy}+Px=Q$

• 3)

The complementary function of (D2+ 4)y = e2x is

• 4)

The particular integral of the differential equation is $\frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } -8\frac { dy }{ dx }$+16y = 2e4x

• 5)

Solution of $\frac { dy }{ dx }$ + Px = 0

#### 12th Standard Business Maths Chapter 3 Integral Calculus – II Important Question Paper - by Sridevi - Sankarankoil - Jul 26, 2019 - View & Read

• 1)

Area bounded by the curve y = x (4 − x) between the limits 0 and 4 with x − axis is

• 2)

The demand and supply functions are given by D(x)= 16 − x2 and S(x) = 2x2 + 4 are under perfect competition, then the equilibrium price x is

• 3)

The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is

• 4)

The given demand and supply function are given byD(x) = 20 − 5x and S(x) = 4x + 8 if they are under perfect competition then the equilibrium demand is

• 5)

The area unded by the curves y = 2x, x = 0 anx=2 is________sq.units.

#### Plus 2 Business Maths Unit 2 Integral Calculus – I Important Question Paper - by Sridevi - Sankarankoil - Jul 24, 2019 - View & Read

• 1)

$\frac { 1 }{ { x }^{ 3 } }$dx is

• 2)

ഽ2xdx is

• 3)

$\frac { sin2x }{ 2sinx } dx$ is

• 4)

$\Gamma \left( \frac { 3 }{ 2 } \right)$

• 5)

$\int _{ 0 }^{ \infty }{ { x }^{ 4 }{ e }^{ -x } }$dx is

#### 12th Business Maths - Applications of Matrices and Determinants Important Question Paper - by Sridevi - Sankarankoil - Jul 18, 2019 - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of m×n matrix whose elements are unity is

• 3)

if T=$_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.4 } & \overset { B }{ 0.6 } \\ 0.2 & 0.8 \end{matrix} \right)$ is a transition probability matrix, then at equilibrium A is equal to

• 4)

if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is

• 5)

Which of the following is not an elementary transformation?

#### frequently asked questions in +2 state board english medium business maths first chapter - by Balamurugan - Jun 29, 2019 - View & Read

• 1)

If A=(1 2 3), then the rank of AAT is

• 2)

The rank of m×n matrix whose elements are unity is

• 3)

The rank of the unit matrix of order n is

• 4)

Rank of a null matrix is

• 5)

For what value of k, the matrix $A=\left( \begin{matrix} 2 & k \\ 3 & 5 \end{matrix} \right)$ has no inverse?

#### twelfth standard business maths chapter one important two mark questions for state board english medium - by Balamurugan - Jun 29, 2019 - View & Read

• 1)

Examine the consistency of the system of equations: x+y+z=7,x+2y+3z=18,y+2z=6 .

• 2)

Find k if the equations 2x+3y−z=5,3x−y+4z=2,x+7y−6z=k are consistent.

• 3)

Find k if the equations x+y+z=1,3x−y−z=4,x+5y+5z=k are inconsistent.

• 4)

Solve the equations x+2y+z=7,2x−y+2z=4,x+y−2z = −1 by using Cramer’s rule

• 5)

The cost of 2kg. of wheat and 1kg. of sugar is Rs 100. The cost of 1kg. of wheat and 1kg. of rice is Rs 80. The cost of 3kg. of wheat, 2kg. of sugar and 1kg of rice is Rs 220. Find the cost of each per kg., using Cramer’s rule.

#### important multiple choice questions in state board english medium business maths chapter one - by Balamurugan - Jun 29, 2019 - View & Read

• 1)

If $\rho (A)$ =r then which of the following is correct?

• 2)

IfA =$\left( \begin{matrix} 1 \\ 2 \\ 3 \end{matrix} \right)$  then the rank of AAT is

• 3)

If the rank of the matrix  $\left( \begin{matrix} \lambda & -1 & 0 \\ 0 & \lambda & -1 \\ -1 & 0 & \lambda \end{matrix} \right)$  is 2. Then $\lambda$ is

• 4)

The rank of the diagonal matrix$\left( \begin{matrix} 1 & & \\ & 2 & \\ & & -3 \end{matrix}\\ \quad \quad \quad \quad \quad \quad \quad \begin{matrix} 0 & & \\ & 0 & \\ & & 0 \end{matrix} \right)$

• 5)

if T= $_{ B }^{ A }\left( \begin{matrix} \overset { A }{ 0.7 } & \overset { B }{ 0.3 } \\ 0.6 & x \end{matrix} \right)$ is a transition probability matrix, then the value of x is